AFFMA

Project "AFFMA" data sheet

The following table provides information about the project.

 Partnership

Take a look of project's partnership.

Map

 Project objective

This research project is concerned with the following three topics in approximation theory and Fourier analysis: 1) Simultaneous approximation of functions and their derivatives in Lp, 0<p<1. We expect to investigate classes of functions and different methods of approximation for which the problem of simultaneous approximation is solvable, and to obtain estimates for the errors of the best approximation of functions and their derivatives for particular methods of approximation in Lp, 0<p<1; 2) New inequalities for moduli of smoothness of functions in Lp, 0<p<1. We expect to find the classes of functions for which the direct and inverse inequalities for moduli of smoothness of functions and their derivatives hold, and to investigate the sharp Ulyanov inequality for different concepts of smoothness; 3) Fourier multipliers and families of multiplier operators in Lp, p>0. We expect to obtain sufficient conditions of the boundedness for such operators in terms of the simultaneous behavior of a multiplier and its derivatives in different functional spaces, and to apply such conditions for solving problems from this proposal.

In our approaches we will combine the methods from approximation theory and Fourier analysis simultaneously, contrary to the previous research concerning the mentioned tasks. Moreover, by using and developing the newly introduced concepts of families of multiplier operators in Lp, 0<p<1, we will provide powerful and universal tools for solving the problems of this proposal as well as for further analysis of operators and related questions in the spaces Lp, 0<p<1.

Working on the proposed research tasks in the teams of very qualified specialists will allow the experienced researcher to enhance his competence in terms of skills acquisition through advanced training, international and intersectoral mobility, to develop a long-lasting research cooperation and to increase the impact of his future activities on European and Ukrainian society.

 Publications